Question 45
Let $m$, $n$, and $p$ be odd positive integers. Prove that the number
$$
\sum_{k=1}^{(n-1)^{p}} k^{m}
$$
is divisible by $n$.
$$
\sum_{k=1}^{(n-1)^{p}} k^{m}
$$
is divisible by $n$.
MathNet 1990 — Part 01 Question 45
Math Olympiad Vault · MathNet 1990 — Part 01